Broadband transformers



May 29, 1962 c, L. RUTHROFF BROADBAND TRANSFORMERS Filed May 12, 1958FIG. 4

WVENTOR C. L RUTHROFF By V% 1 ATTORNEY United States Patent G" 3,037,175BROADBAND TRANSFORMERS Clyde L. Ruthrolf, Fair Haven, N.J., assignor toBell Telephone Laboratories, Incorporated, New York, N.Y., a corporationof New York Filed May 12, 1958, Ser. No. 734,751 3 Claims. (Cl. 333-32)This invention relates to impedance transforming devices and, moreparticularly, to broadband bifilar Wound autotransformers.

The problem of distortionless transmission of signals over wires is anold one, encountered often in electrical communications systems. As therange of operating frequencies is extended, as is the current trend,this prob lem has become more and more acute. For example, in order tosupply gain for pulses of millimicroseconds duration, amplifiers andcoupling transformers with bandwidths of hundreds of megacycles areneeded. While the problem of extending the frequency range oftransformers has received the attention of many investigators, and somesuggestions and improvements have been made, currently availabletransformers still fall far short of fulfilling the bandwidthrequirements presently encountered in the electronic arts.

The difficulties in providing broadband transformers is due in greatpart to the series self-inductance and parasitic inter-windingcapacitance of the transformer windings themselves. For example, in aconventionally wound transformer, the upperend of the pass band isgenerally determined by the large interwinding capacity which resonatesat some relatively low frequency, while the low frequency end of thepass band is limited by a relatively small coil inductance which appearsas a low impedance in parallel with the signal source. While theselimitations have been somewhat overcome by the use of miniatureconstruction and new and improved magnetic core materials, this type ofapproach to the problem has enjoyed only limited success.

The theory of transmission lines, which has been well developed in thecommunications art, on the other hand, has indicated how this problemmay be attacked by means of a more fundamental and promising approach.It is known that a pulse can be propagated down a transmission linewithout distortion, and that the input impedance of any length ofproperly terminated l-ine is a pure resistance. Thus, for instance, aLecher wire line having the desired characteristic impedance can bewound on a core form so that the conductors are distributed over thesurf-ace of the core with the two conductive members forming a bifilarwound transformer having a 1:1 turns ratio. One end of the biiilar coilcomprises the input or primary end of the transformer, and the other endthe output or secondary end. In such an arrangement, the seriesinductances and interwindin'g capacitances, which normally set thefrequency limits for the conventional lumped parameter transformer, arenow part of a dis tributed transmission line system. If the line isproperly terminated with a pure resistance, which may readily becomputed in terms of the line constants, a 1:1 impedance transformer ofunusually broad bandwidth is obtained.

Such distributed transformers have been used in the past, but since theimpedance transformation ratio is only 1:1, it is necessary to useseveral such coils where impedance transformations greater than 1:-l aresought. In particular, where an impedance transformation of 4:1 isdesired, two bifilar coils have to be used. Furthermore, where animpedance transformation of 4:1 is sought to connect two unbalancednetworks, an additional, or third coil, has to be added to the twoabovementioned coils. In such multiple coil arrangements,

3,037,175 I Patented May 29, 1962 2 w some saving in space andmaterialis affected by winding all the coils on a common core. This maybe done since the net magnetic field resulting from the flow of signalcurrent is zero, and consequently there is no magnetic coupling amongthe several coils even though they share a common magnetic core. Themagnetizing current, however, does produce a net magnetic field.Consequently, by winding the several coils series aiding for themagnetizing current, there is a net increasein the number of coupledturns, and the corresponding increase in the effective transformerinductance. This has the effect of extending the low frequency end ofthe transformer pass band. The difliculty with such an arrangement,however, resides in the care which must be taken in winding thetransformer so as to minimize the interwinding capacitance among thecoils since this capacitance will adversely affect the high frequencyresponse.

It is, therefore, an object of this invention to produce broadbandimpedance transformation ratios greater than 1:1 using a single bifilarwound-coil.

It is a further objective of this invention that said trans formationratios be obtainable in a transformer used to couple two unbalancedsystems.

If the length of the conductors making up the .bifilar coil is anappreciable part of a wavelength of the signal transmitted through thetransformer, the input impedance to the transformer will be a functionof the length of the conductors as well as the load impedance. Since itis desirable for matching purposes that the terminal impedances of thetransformer be only a function of the load impedance and the-transformerturns ratio, it is an additional object of this invention to providebroadband impedance transformation means which are substantiallyindependent of the signal frequency over an extended range of operatingfrequencies.

A transformer constructed in accordance with the invention comprises apair of insulated conductive wires, uniformly spaced from each other andwound together in a substantially helical form. A coil so wound has thedistributed properties of a uniform transmission line and thecorresponding broadband capabilities when used as a transformer. Animpedance transformation ratio of 4:1 is obtained by serially connectingthe coils by conductively joining one end of one of the conductors tothe other end of the other conductor and by making connections to andfrom the transformer whereby one of the external circuits is connectedacross only one of the coiled conductors and the other external circuitis connected across both of the coiled conductors.

It is a feature of the present invention that by merely rearranging theground connections, the transformer may be used either to connect twounbalanced networks or to connect an unbalanced network to a balancednetwork without the further cascading of an additional coil, whichaddition tends to decrease the overall bandwidth.

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It is a further feature of the invention that by using core material ofsufficiently high permeability, the number of turns may be reduced for agiven low frequency response, and the length of line constituting thebifilar coil made small. Since the transformer output is zero at thehigh frequency end of the transformer pass band when the electrical linelength is a half of a wavelength of the signal frequency, using fewerturns has the effect of extending the upper end of the transformerresponse characteristic. Furthermore, since the input impedance of ashort length of transmission line is approximately equal to the loadimpedance terminating the line, the transformer is substantiallyindependent of the line characteristics, and free of transmission lineelfects over a major portion of the transformer pass band. A transformerconstructed and operated in accordance with the teachings of theinvention has the broadband characteristics of a parallel wiretransmission line and the impedance transformation characteristics of acenter-tapped autotransformer.

These and other objects, the nature of the present invention, and itsvarious features and advantages will appear more fully uponconsideration of the various specific illustrative embodiments shown inthe accompanying drawings and analyzed in the following detaileddescription of these drawings.

In the drawings:

FIG. 1 shows diagrammatically a bifilar wound autotransformer connectedin accordance with the principles of the invention;

FIG. 2 is a schematic illustration of the transformer of FIG. 1 whenused to connect two unbalanced networks;

FIG. 3 is a schematic illustration of the transformer of FIG. 1 whenused to connect an unbalanced network and a balanced network;

FIG. 4 shows diagrammatically a bifilar autotransformer using twocascaded coils wound on a common magnetic core.

Referring to the accompanying drawings, and more specifically to FIG. 1,there is diagrammatically shown a transformer wound and connected inaccordance with the present invention. The transformer comprises a pairof insulated conductive filaments 11 and 12, wound together in asubstantially helical form over coil form 10. Insulated filaments 11 and12 are arranged so that their insulated coverings are in closejuxtaposition substantially throughout their entire lengths. Thejuxtaposition or contiguous arrangement of these two wires is such as toproduce substantially unity coupling between the two windings and, inaddition, to produce the equivalent of a uniform parallel wiretransmission line from one end of the coil to the other end thereof. Thedouble threaded spiral or helical coils described above are known in theart as bifilar coils and will be referred to as such hereinafter. Theactual spacing of the conductive portions of members 11 and 12, and thediameter of said conductors, will be considered in greater detail below.

The bifilar coil is mounted upon a coil form which may be composed ofany suitable high permeability, low loss core material. For example, anumber of transformers using nickel-zinc ferrite cores have beenconstructed and have given very satisfactory results. While coil form 10has been shown as a toroidal member, it may assume any convenient shapeconsistent with the electrical requirements of the transformer windings.

An impedance transformation ratio of 1:4 is obtained by seriallyconnecting coilsll and 12 by joining one end 4 of coil 12 to the otherend 1 of coil 11, and by connecting external circuit 13 to ends 1 and 2of coil 11, and by connecting the other external circuit 14 to ends 2and 3. Thus connected, circuit 13 is across one of the bifilar coils,and circuit 14 is across the two serially connected coils, and thetransformed impedance seen by circuit 13 is one-fourth the impedance ofcircuit 14.

In FIG. 2 there is shown a schematic diagram of the transformer of FIG.1 and its associated external circuits in which network 13 of FIG. 1more specifically comprises a signal generator 23 and its equivalentinternal impedance R and network 14 is represented by load resistor RResistor R is equal to 4R and is to be matched to the generatorimpedance by means of transformer T. The transformer comprises theserially connected bifilarly wound coils 21 and 22, of which end 1 ofcoil 21 is connected to end 4 of coil 22. The generator 23 andresistance R are connected across ends 1 and 2 of coil 21, and loadresistor R is connected across ends 3 and 2 of the serially connectedcoils 21 and 22. So connected, generator 23, resistance R and coil 21form a first current mesh, and generator 23, resistance R coil 22 andload resistor R form a second current mesh.

An analysis of the operation of the invention may best be had byconsidering the low frequency and high fre- 4. quency operationseparately. At low and at intermediate frequencies, ordinary lumpedparameter network analysis is used. In the high frequency region,transmission line techniques are resorted to.

Designating the reactance of each half of the bifilar winding as X=wL,and the mutual inductances as kX, where k is the coefficient ofcoupling, the low frequency and intermediate frequency mesh equationsare given as follows:

where A=X (k 1)+jX[2R (1-]-k) +R ]+R,,R

Examining the load current, I more carefully, it follows that:

Since 4R =R and kzl:

and

From Equation 5, the low frequency half power point is obtained when:

Thus, if the low frequency half power point is designated as frequencyh, the individual coil inductance L is given as:

RE The ratio of generator to load current is:

l 1+I2I r2| 4+ X(l+k) (8) Since over the major portion of the pass bandX(1+k) is much greater than R the transformer has a 2:1 current ratio,and 1 :1

The output voltage V is given as:

However, since kzl, V =V =V and V =2V the output voltage is twice theinput voltage, and the transformer has a 1:2 voltage step-up ratio. Asthe ratio of input voltage to input current is one-fourth the loadvoltage to current ratio, the transformer is matched when R ==4R as wasindicated above.

As the operating frequency is raised, the output voltage is againexpressed as the sum of V and V thus:

assay/* The voltage V however, is the same as the input voltage V whichvoltage appears across one end of the bifilar winding, and drives thebifilar as a transmission line. V then is merely the voltage V which haspassed through a length, l, of transmission line. T e load voltage maythen be rewritten as:

where B is the phase constant, and l the length of each of theconductors making up the bifilar winding. The ratio of the input voltageV to the load voltage V is then:

From Equation 9 it is evident that the transformer output is zero whenthe conductor lengths, l, are one-half of a wavelength long.

The important equations to note are Equations 7 and 9, since it is theseequations which fix the low frequency and high frequency cut-off pointsand thus define the transformer band pass.

While the transformer operation over a major portion of the pass band issubstantially independent of the transmission line characteristics ofthe bifilar coil, the line characteristics do influence the transformeroperation at those frequencies where the line lengths, l, are comparableto a quarter of a wavelength of the operating frequencies. At these highfrequencies, the power transfer through the transformer is affected bythe characteristic impedance of the bifilar coil. It can be shown, thatfor maximum power transfer, the characteristic impedance of thetransmission line, formed by the two conductors comprising the bifilarcoil, is equal to the geometric mean of the input and output impedances:

Thus, where the input impedance is R and the output impedance is 4R thecharacteristic impedance of the coil is given as:

In terms of the wire size and spacing:

where p. is the effective permeability e is the effective dielectricconstant 11 is the distance between wire centers and a is the wirediameter.

In FIGS. 1 and 2, both external networks 13 and 14 were single ended orunbalanced with respect to ground. In FIG. 3, the transformer is used toconnect an unbalanced network 33 to a double ended or balanced network34, 34'. This is accomplished simply by grounding the interconnectedterminals 1 and 4 of coils 31 and 32 respectively. As in FIGS. 1 and 2,one of the external circuits is connected between terminals 2 and 1,while the second external network is connected between tenninals 2 and3. Since the latter circuit is balanced with respect to ground, it isshown as comprising two equal portions, 34 and 34'.

In FIG. 4 a pair of cascaded bifilar autotransformers T and T forproducing a 1:16 impedance transformation ratio are shown wound on acommon core 41). Each of the bifilarly wound coils comprises a parallel'wire .transmission line, each of which is wound into a double threadedspiral or helical form on said core. Transformer T consists of winding41, having terminals 1 and 3, and winding 42., having terminals 2. and4. Adjacent terminals 1 and 2 make up one end of the transformer andadjacent terminals 3 and 4 the other end. Coils 41 and 42 are seriallyconnected by connecting end 1 of coil 41 to the other end 4 of coil 42.

Transformer T consists-of winding 45, having terminals 6 and 8, andwinding as, having terminals 5 and 7. Adjacent terminals 7 and 8 make upone end of transformer T and adjacent terminals 5 and 6 the other end.Coils 4S and 4e are serially connected by connecting end 8 of coil 45 tothe other end 5 of coil 46.

External network 43 is connected across coil 41 by connecting toterminals 1 and 3 of coil 41. Transformer T comprising the secondexternal network for transformer T is attached to transformer T byjoining terminal 5 to terminal 2, and joining terminal 7 to terminal 3'.So connected, coil 46 of transformer T is attached across the seriallyconnected coils 41 and 42. External network 44, constituting the secondimpedance across transformer T is connected across the seriallyconnected coils 45 and 46 by attaching network 44 to terminals 6 and 7.Since each of the transformers T and T has a 1:4 impedance step-upratio, for matched conditions, network 44 should have an internalimpedance sixteen times the impedance of network 43.

As indicated above, the characteristic impedance of the bifilar windingsfor optimum high frequency operation, is equal to the geometric mean ofthe impedances of the external networks connected across thetransformer. If the impedance of network 43 is R, then the matchedimpedances across transformer T1 are R and 4R, and the characteristicimpedance of the bifilar winding of transformer T is 2R. Similarly, thematched impedances across transformer T are 4R and 16R, and thecharacteristic impedance of the bifilar Winding of transformer T2 IS 8R.

In all cases, it is understood that the above-described arrangements aresimply illustrative of a small number of the many possible specificembodiments which can devised in accordance with these principles bythose skilled in the art without departing from the spirit and scope ofthe invention.

What is claimed is:

I. In combination, a two-element transmission line having acharacteristic impedance Z comprising a pair of conductively insulatedwires Wound together in a substantially helical form, said wires beingcontiguous and parallel from a first end of each to the second end ofeach to form a a pair of coils, said coils being serially connected withthe first end of one being connected to the second end of the other, aninput circuit and an output circuit, one of said circuits havinganimpe'dan'ce R connected across both of said serially connected coils,and the other of said circuits having an impedance R connected acrossone of said coils, wherein said'characteristic impedance and saidcircuit impedances are'related by OW l Z 2. The combination 3.-Thecombination according to claim' 2 wherein R =41rf L, where L is theinductance of each of said coils and f is the low frequency half powerpoint.

according to claim. 1 wherein References Cited in the file of thispatent UNITED STATES PATENTS 1,762,775 Ganz June ll), 1930 2,654,836Beck Oct. 6, 1953 I 2,735,988 Fyler Feb. 21, 1956 2,788,495 Hylas Apr.9, 1957'

